y=14^(–4/x) find dy/dx.?

Answer 1

y = 14^(-4/x)

This is a bit tricky, so let's change the exponent to something more obviously differentiable.

y = 14^( -4(1/x) )

Note that the derivative of 1/x is -1/x^2, and that when constants are next to functions, they can be ignored when taking derivatives. Also, note that the derivative of a^x is a^x ln(a). Therefore,

dy/dx = 14^ ( -4(1/x) ) ln(14) [(-4)(-1/x^2)]

Simplifying this, we get

dy/dx = (4/x^2) (14^(-4/x)) ln(14)

Answer 2

Using logarithmic differentiation

y=14^(–4/x)

take natural log of both sides
ln y = (-4/x) ln 14

differentiate implicitly
(1/y) dy/dx = -4 ln 14)/-x^2
(1/y) dy/dx = 4 ln 14/x^2

solve for dy/dx by multiplying by y
dy/dx = (y* 4 ln 14)/x^2

substitute original equation for y

dy/dx = (14^(–4/x) * 4 ln 14)/x^2

Answer 3

You guys or gals are so smart. I'm jealous. Even though I am a very good reader and love English and History, wish I could do math.